Authors: Horiuchi, Kiyomitsu
Šešelja, Branimir
Tepavčević, Andreja 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Trice-valued fuzzy sets: Mathematical model for three-way decisions
Journal: Information Sciences
Volume: 507
First page: 574
Last page: 584
Issue Date: 1-Jan-2020
Rank: M21a
ISSN: 0020-0255
DOI: 10.1016/j.ins.2018.09.007
Abstract: 
Under the idea to develop a mathematical model for three-way decisions, the aim of the paper is to study trice-valued fuzzy sets, i.e., mappings from a set to a structure called a trice. A trice is a triple semilattice satisfying roundabout absorption laws, suitable for representing multi-dimensional orders, which appear in complex movements in a plane or in a space. Our approach is cutworthy, namely, we investigate cuts of such fuzzy sets and prove theorems of decomposition and synthesis. This new notion provides a possibility to capture vague triangular situations. Therefore, a motivation for our research is to provide a new algebraic and order-theoretic model for three-way decisions, as this topic has been introduced recently for solving particular human problems and for information processing.
Keywords: Cuts | Shadowed sets | Three-way decisions | Trice | Trice-valued fuzzy sets | Triple semilattice
Publisher: Elsevier
Project: Development of methods of computation and information processing: theory and applications 
Provincial Secretariat for Higher Education and Scientific Research, Grant no. 142-451-3642/2017/01

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